06 February 2011

Correlation in betting on the NFL.

Nate Silver points out that just because the spread in today's Super Bowl is small (the Packers are something like a three-point favorite) doesn't mean that the game will necessarily be close. It just means that it's almost equally likely to be a blowout in one team's favor as in the other's.

Not surprisingly, though, the regression line for margin of victory, as predicted from point spread, is very close to having slope 1 and passing through the origin. As it should, because otherwise bettors would be able to take advantage of it! Say that 7-point favorites won, on average, by 9 points. Assume that the distribution of actual margin of victory, conditioned on point spread, is symmetrical; then half of 7-point favorites would win by 9 points or more, so more than half would win by 7 points or more, and one could make money by betting on them. On the other hand, say that 7-point favorites won, on average, by 5 points; then you could make money by betting agsinst them.

(For what it's worth, I don't have a particular interest in this game. In fact I probably won't even watch it. I have no connection to either Pittsburgh or Green Bay, and as longtime readers know, I'm a baseball fan.)